The goal of the present project is to derive a new theory for the design of heat transfer systems with twisted paths, a theory capable to analyze and predict the architecture of the heat transfer system with reduced thermal resistance, reduced pumping energy requirements, lower conductive material consumption, and consequently lower cost. The design methodology considers two geometric degrees of freedom: (1) hierarchy of components, that is, few large & many small, and (2) geometrical twist of the main energy paths. These aim to reduce the global thermal resistance to energy flow. If successful, the project can impact the cost of many energy systems by reducing their thermal resistance, pumping energy requirements, and conductive material consumption. The design methodology presented in this project has the potential to accelerate heat transfer technology evolution ranging from aerospace to biomedical systems. This project involves a postdoctoral scholar and one undergraduate student is to be supported through the Research Experiences for Undergraduates (REU) supplement program. This project contributes to the design of thermal management systems by creatively integrating theoretical and numerical approaches with the rigorous design principle of Constructal Law. The considered design system is a slender heat transfer component (fin, channel, etc.) and its unique geometrical form of twisted shape. This project advances the state-of-the-art of current constructal theories in thermal design by introducing the twisted geometry as a new degree of freedom in constructal design. This new transformative consideration can allow the design to morph and evolve more easily, yielding a high-risk/high-payoff condition if successful.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.